I am never buying another betta online....this whole experience is too stressful.

Anyway, I got him around 11am yesterday and acclimated him over several hours before releasing him. His tank is 2.5 g, heated, used conditioner.

I keep the tank mostly covered with a towel to keep it dark.

Woke up this morning to find him partially out of the water because he wedged himself behind the heater. I moved the heater to the middle of the tank and he is now pale and just laying around, coming up to breathe.

Oh no! I'm so sorry to hear that. Please don't kick yourself nor blame yourself, things happen.
There have been many instances where a betta had been out of water for hours and end up living. He was partially out? He's probably stressed more then anything at this moment.. if your heater was warm to the touch when you moved it, he may have gotten heated up.

If you have tannins, IAL, dried oak leaves I would add that in, as well as stress coat since it will help rebuild any loss slime coat as well as soothe him. Otherwise, I would keep his light off in his tank and hope he has the will and strength to keep going.

Ohhhh man, I am soooooooo sorry for your loss. That has to be so frustrating, especially after spending alot of money and waiting patiently for the fish to get here =( I am so sorry, I hope the rest of your birthday is better!